The citation style will deal with that..just make sure that you have two-field mode on and that the family name is in the right field and the first name(s) in the other, either short or full. Zotero will do the abbreviation for you.
You can always test it works in a fresh document. If you see extra letters you might just have citations with the same name and the citation style disambiguation kicks in. See https://www.zotero.org/support/kb/given_name_disambiguation

You say the family name is in the right field and the first name(s) in the other, however, the two-field option for Author has a blank box on the left and the box next to it says (first) on the right. I'm assuming this means the family name is on the left and the first name is on the right. Is that what you meant?

Just show me how it should look i.e. for an author named Joe Bloggs is it entered as:
J Bloggs
Bloggs J
J.Bloggs
Bloggs. J
J, Bloggs
Bloggs, J
J, Bloggs.
Bloggs, J.

Explicitly show me the order and what punctuation is required, please.

I changed all my references of the same name to the same format e.g. G Vogt but the in-text citation is (G Vogt 2021). So I changed them all to G, Vogt 2021 and they looked like this (G, Vogt 2019) in the document.

So what exactly should it look like in Zotero?

Couple Qu's, If you change the format in My Library does it change throughout your collection? Is there a quick way to change all the formats of a single author from multiple references/papers

Early on in this thread and in the documentation is the recommendation that when the same author is in Zotero with names that are more or less complete (Lastname Firstmame(s) in two-name 'double box' Zotero fields*: Bloggs, Joe; Bloggs, Joseph; Bloggs, Joseph Alan; Bloggs, Joseph A.) the names should be edited so that every entry is the most complete name regardless of how the name appeared above each publication (all must be entered as, Bloggs, Joseph Alan).

This is particularly important when using a Chicago style. See my comment in another recent thread:
https://forums.zotero.org/discussion/115879/how-to-fix-inconsistent-author-names-in-zotero#latest

It was also required in earlier APA style guides but no longer.

[edit: There are authors with quite common names. What I find creepy is when there are different unrelated authors with exactly the same full name who are contemporaneously writing about the same subject but who are in different professional disciplines.]

It can be very tedious to find author names that need editing and to do the edits. Through the years there have been comments for changes to the program or for plug-ins. But even with a utility to facilitate identifying and editing author names there will still need to be some human decision-making needed. An author named Jennifer Alice Bloggs who is listed in the article metadata shouldn't be confused with Joe who was mentioned above -- even though the journal provided her name as Bloggs, J.A.

This is a well-recognized problem for keeping names straight in databases (not just Zotero). Author authority services (ORCID, ResearcherID, VAIF) have been introduced but as adamsmith mentioned in the thread I linked to above (and I have grumbled about in other threads) these haven't solved the problem. There are a few online databases that try to expand author names so that all names are listed as the most complete version, or like Scopus and assign an alphanumeric identifier that will keep all authored items together while listing the author name as published.

This could become an essay about identifying names in need of disambiguation but this isn't the place for it. Name disambiguation is essential but tedious to perform in your database.

*edit: the 'one box' name field shouldn't be used for individuals with more than one name but should be for agency or institution names (CERN, RAND Corporation, World Bank, International Labor Organization). It can be used for mononymous named people (Plato, Socrates, and maybe Sting?Modonna?).

No problem (sorry first time using this forum). Very special thank you for all your time and assistance wih this. x